On the stove top, heat a small nonstick frying pan over medium-high
heat. Squeeze the sausage meat out of the casing into the frying pan
(discard the casing). Cook, breaking up the sausage with a wooden spoon,
until the meat is lightly browned all over. Remove from the pan.

Set the pita bread on a baking sheet. Sprinkle on the mozzarella
cheese, then the sausage, asparagus and thyme. Top with grated
Parmigiano-Reggiano, then a bit of black pepper.

Place the baking sheet in the oven and bake for 10 minutes. Remove
from the oven (do not turn the oven off).

Without breaking the yolk, carefully crack the egg into a small bowl.
Then slide the egg onto the center of the pizza. Return the pizza to
the oven and cook for 10 minutes, or until the egg white is just set and
the yolk is still runny. Remove from the oven, sprinkle with more
pepper, and serve hot.